"We will carefully examine the facts contained in the indictment and answer the quesion as to whether or not the governor can lead our state while a felony case moves forward," the chamber's top GOP leaders said in a statement.

The charges stem from an extramarital affair Greitens had before being elected governor in 2016. Greitens has admitted to the affair, but he has denied accusations of a blackmail scheme from the woman's ex-husband. The woman has refused to speak publicly about the matter. On a recording the ex-husband made without her knowledge, she quoted Greitens as saying, "You're never going to mention my name, otherwise this picture will be everywhere."

Greitens had refused to confirm or deny whether he took a picture of the woman.

The indictment charges him with felony invasion of privacy, stating that he "knowingly photographed [the woman] in a state of full or partial nudity" without her consent, where she had a reasonable expectation of privacy. The indictment further states that Greitens transmitted the photograph electronically.

"The law makes it a felony if a person transmits the image contained in the photograph or film in a manner that allows access to that image via a computer," St. Louis Circuit Attorney Kim Gardner said in a statement.

Greitens was booked and released on Thursday. A hearing has been set for March 16.

If convicted, Greitens could face up to four years in prison. But invasion of privacy charges are difficult to make stick.

"The charges against my client are baseless and unfounded," Greitens' attorney Edward L. Dowd Jr. said in a statement. "My client is absolutely innocent. We will be filing a motion to dismiss."

On Facebook, Greitens wrote that he had "made a personal mistake" but "did not commit a crime." He called Gardner a "reckless liberal prosecutor who uses her office to score political points."

Gardner, a Democrat, was working against a deadline, with a three-year statute of limitations on the charge due to run out next month.

Since becoming governor just over a year ago, Greitens has managed to alienate many legislators, including members of his own party. He made a habit of criticizing legislators by name on social media, while outside groups affiliated with him ran negative ads against those who crossed the governor. His own agenda -- including his recent push for a sizable tax cut -- has mostly stalled.

"He’s burned so many bridges, GOP lawmakers might see this as their opening to force him to resign," says John Messmer, a political scientist at St. Louis Community College who is running for Congress as a Democrat. "Rumors and gossip is one thing. Legal charges might be a game-changer."

Indeed, two additional GOP legislators called for Greitens to resign Thursday.

"In the wake of the grand jury criminal indictment, and with legal proceedings to come, I cannot see how he could effectively perform the duties of his office, let alone to lead with the kind of moral authority needed to make a positive impact," state Rep. Kevin Corlew wrote on Facebook.

Republican state Rep. Nate Walker, an early Greitens supporter, was among five GOP legislators who called on Greitens to resign last month. In the wake of the indictment, he said his fears that Greitens would continue to be wounded by bad news had been confirmed.

On Thursday, GOP state Sen. Rob Schaaf tweeted, "...he's done," apparently completing a thought he'd tweeted on Jan. 10, the night the news of the affair first broke: "Stick a fork in him."

Gail McCann Beatty, the Democratic floor leader in the state House, also urged him to step down on Thursday.

"It will be extremely difficult for the governor to effectively do his job with a felony indictment hanging over his head," she said in a statement.

Greitens canceled a planned trip to Washington for a meeting of the National Governors Association this weekend. He has spent some time seeking to mend political fences in recent weeks, but he has not signaled any intention to step down.

"Many in Jefferson City view everything associated with St. Louis as purely motivated by Democrats with an ax to grind," Messmer says, "so his supporters might blow this off as purely politically motivated."

In Missouri, indictment proceedings would begin in the state House. If the House were to approve articles of impeachment, the case would then be tried by "seven eminent jurists" who would be elected by the state Senate.

Greitens may never be impeached, but the indictment makes his road to political recovery that much steeper.

"Greitens doesn't have a lot of friends in the Missouri Legislature," says Warren, the St. Louis University political scientist. "There are a lot of people who wouldn't mind dumping him."